关于最优投资组合和生态平衡的新观点
A new spin on optimal portfolios and ecological equilibria
摘要：
我们考虑经典问题的最优投资组合建设的约束，没有空头头寸是允许的，或等价的有效平衡的多物种Lotka-Volterra方程的自我调节的特殊情况下，相互作用矩阵是单位秩，对应于物种竞争一个共同的资源。我们计算的平均数的解决方案，并表明其对数增长$N^α$，其中$N$是资产或物种的数量和$α\leq 2/3$依赖于相互作用矩阵分布。我们推测，最可能的解决方案的数量要小得多，并与典型的稀疏性$m(N)$的解决方案，我们明确计算。我们还发现，解决方案的景观是类似的自旋玻璃，即非常不同的配置是准简并。与此相对应，“无序混沌”也存在于我们的问题中。我们讨论了这样一个属性的投资组合建设和生态的后果，并质疑理性决策的意义时，有一个非常大的数量“满意”的解决方案。
英文摘要：
We consider the classical problem of optimal portfolio construction with the constraint that no short position is allowed, or equivalently the valid equilibria of multispecies Lotka-Volterra equations with self-regulation in the special case where the interaction matrix is of unit rank, corresponding to species competing for a common resource. We compute the average number of solutions and show that its logarithm grows as $N^α$, where $N$ is the number of assets or species and $α\leq 2/3$ depends on the interaction matrix distribution. We conjecture that the most likely number of solutions is much smaller and related to the typical sparsity $m(N)$ of the solutions, which we compute explicitly. We also find that the solution landscape is similar to that of spin-glasses, i.e. very different configurations are quasi-degenerate. Correspondingly, "disorder chaos" is also present in our problem. We discuss the consequence of such a property for portfolio construction and ecologies, and question the meaning of rational decisions when there is a very large number "satisficing" solutions.
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